Finite Group Databasebeta

← #14643531

Subgroups — #14643531

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077246C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13066473C211yesmaximal, characteristic, complemented
5#13066472C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622600—21no—
13#10622590—21no—
14C4×(C2×D11)⋊C4C412yes—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622545C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622450C412yescomplemented
20#10622448—21no—
21#10622446C412yescomplemented
22D11×C4⋊C8—21no—
23#10622339—21no—
24D11×C22⋊C8—21no—
25#10622332—21no—
26#10622331—21no—
27#10622320—21no—
28#10622318—21no—
29#10622318C412yescomplemented
30D11×#97C412yescomplemented
31#10622277—21no—
32#10622264—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4×Dic11C2×C412yes—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4313—22no—
46C2×C8×D11—22no—
47C42×D11C2×C411yescharacteristic
48C42×D11C2×C411yescharacteristic
49C42×D11C2×C411yescharacteristic
50C42×D11C2×C411yescharacteristic
51C42×D11D411yescharacteristic
52C42×D11D411yescharacteristic
53C42×D11Q811yescharacteristic
54C42×D11Q811yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8C2×C412yes—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97C2×C412yes—
61C11×#95—21no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68(C2×D11)⋊C8—22no—
69(C2×D11)⋊C8—22no—
70#66879—22no—
71Dic11⋊C8—22no—
72Dic11⋊C8—22no—
73C8×Dic11—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)C2×C412yes—
76#66867—21no—
77#66867C2×C412yes—
78#7951—111nomaximal, Sylow
79C23×D11C22⋊C411yescharacteristic
80C22×C4×C11—22no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C4×D11C4211yescharacteristic
93C2×C4×D11C4211yescharacteristic
94C2×C4×D11C22⋊C411yescharacteristic
95C2×C4×D11C22⋊C411yescharacteristic
96C2×C4×D11C22⋊C411yescharacteristic
97C2×C4×D11C22⋊C411yescharacteristic
98C2×C4×D11C4⋊C411yescharacteristic
99C2×C4×D11C4⋊C411yescharacteristic
100C2×C4×D11C4⋊C411yescharacteristic
101C2×C4×D11C4⋊C411yescharacteristic
102C2×C4×D11C4⋊C411yescharacteristic
103C2×C4×D11C4⋊C411yescharacteristic
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C11×C4⋊C4—42no—
107C42×C11—42no—
108C42×C11C22×C411yescharacteristic
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×Q811yescharacteristic
112(C2×D11)⋊C4—44no—
113C4⋊Dic11—42no—
114C4×Dic11—42no—
115C4×Dic11C4211yescharacteristic
116C4×Dic11C4211yescharacteristic
117C4×Dic11C22⋊C411yescharacteristic
118C4×Dic11C22⋊C411yescharacteristic
119C4×Dic11C22⋊C411yescharacteristic
120C4×Dic11C22⋊C411yescharacteristic
121C4×Dic11C4⋊C411yescharacteristic
122C4×Dic11C4⋊C411yescharacteristic
123C4×Dic11C4⋊C411yescharacteristic
124C4×Dic11C4⋊C411yescharacteristic
125C4×Dic11C4⋊C411yescharacteristic
126C4×Dic11C4⋊C411yescharacteristic
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129#4313—44no—
130C8×D11—44no—
131#2920—111no—
132C2×#432—111no—
133#2283—111no—
134#1285—111no—
135#1285—111no—
136#1285—111no—
137#1285D1111yescharacteristic, complemented
138C23×C11C2×C22⋊C411yescharacteristic
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—22no—
142C22×D11—41no—
143C22×D11#9511yescharacteristic
144C22×D11#9511yescharacteristic
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11C2×C4211yescharacteristic
153C2×C4×C11C2×C22⋊C411yescharacteristic
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C2×C4⋊C411yescharacteristic
156C2×C4×C11C2×C4⋊C411yescharacteristic
157C2×C4×C11C2×C4⋊C411yescharacteristic
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11#9511yescharacteristic
166C2×Dic11#9511yescharacteristic
167C2×Dic11#9511yescharacteristic
168C2×Dic11#9511yescharacteristic
169C2×Dic11#9511yescharacteristic
170C2×Dic11#9511yescharacteristic
171C4×D11—22no—
172C4×D11—22no—
173C4×D11—22no—
174C4×D11—22no—
175C4×D11—41no—
176C4×D11—41no—
177C4×D11—41no—
178C4×D11—41no—
179C4×D11—41no—
180C4×D11—41no—
181C4×D11—41no—
182C4×D11—41no—
183C8×C11—42no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C22×C42—111no—
188#432—111no—
189#432—112no—
190#432—111no—
191#432—221no—
192#432—221no—
193#432—221no—
194#432C2×D1111yescharacteristic
195#432C2×D1111yescharacteristic
196#431—112no—
197#431—221no—
198#423—112no—
199C2×C4⋊C8—221no—
200#407—221no—
201C2×C22⋊C8—221no—
202C4×M16—221no—
203C2×#97—112no—
204#383—221no—
205#382—221no—
206#381—221no—
207#380—221no—
208C4×C4⋊C4—111no—
209C4×C4⋊C4C2×D1111yescharacteristic
210C4×C22⋊C4—112no—
211#376—112no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11C2×#9511yescharacteristic
215C22×C11#41311yescharacteristic
216C22×C11#41311yescharacteristic
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—21no—
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11H(3,ℤ/4)12yes—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—82no—
231C4×C11#42112yes—
232Dic11—21no—
233Dic11—21no—
234Dic11—21no—
235Dic11—21no—
236Dic11—21no—
237Dic11—21no—
238Dic11—82no—
239C23×C4—111no—
240C23×C4—111no—
241C23×C4—111no—
242C2×M16—222no—
243C22×C8—222no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—221no—
246C2×C22⋊C4—222no—
247C2×C42—111no—
248C2×C42—111no—
249C2×C42—111no—
250C2×C42—111no—
251C2×C42—111no—
252C2×C42—111no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—111no—
258C2×C42—112no—
259C2×C42C4×D1112yes—
260C2×C42C22×D1111yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—112no—
263C4⋊C8—222no—
264C4⋊C8—222no—
265C4⋊C8—221no—
266C4⋊C8C4×D1112yes—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—222no—
270C22⋊C8—222no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273#97—21no—
274#97—112no—
275#97—222no—
276#97—221no—
277#97C4×D1112yes—
278C4×C8—222no—
279#95—21no—
280#95—222no—
281#95—222no—
282#95—222no—
283#95—221no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11C2×H(3,ℤ/4)11yescharacteristic
287C2×C11#173311yescharacteristic
288C2×C11#174211yescharacteristic
289D11—22no—
290D11—41no—
291C24—111no—
292C22×C4—22no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—222no—
309C22×C4—442no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—442no—
313C22×C4C2×C4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316M16—444no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—444no—
322C4⋊C4—42no—
323C4⋊C4—442no—
324C22⋊C4—444no—
325C42—42no—
326C42—111no—
327C42—111no—
328C42—111no—
329C42—111no—
330C42—111no—
331C42—111no—
332C42—111no—
333C42—111no—
334C42—111no—
335C42—111no—
336C42—111no—
337C42—111no—
338C42—442no—
339C42C2×C4×D1111yescharacteristic
340C42C2×C4×D1111yescharacteristic
341C42D4×D1111yescharacteristic
342C42Q8×D1111yescharacteristic
343C11#795111yescharacteristic, complemented, Sylow
344C23—111no—
345C23—111no—
346C23—222no—
347C23—221no—
348C23—221no—
349C23—441no—
350C23C22⋊C4×D1111yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—111no—
359C2×C4—111no—
360C2×C4—111no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—111no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4C42×D1111yescharacteristic
384C2×C4C22⋊C4×D1111yescharacteristic
385C2×C4C22⋊C4×D1111yescharacteristic
386C2×C4C4⋊C4×D1111yescharacteristic
387C2×C4C4⋊C4×D1111yescharacteristic
388C2×C4C4⋊C4×D1111yescharacteristic
389C8—42no—
390C8—42no—
391C8—442no—
392C8—442no—
393C22—21no—
394C22—21no—
395C22—112no—
396C22—221no—
397C22—221no—
398C22—221no—
399C22—221no—
400C22—221no—
401C22—442no—
402C22—442no—
403C22D11×#9511yescharacteristic
404C22#1062235811yescharacteristic
405C22#1062236411yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—221no—
413C4—221no—
414C4—221no—
415C4—221no—
416C4—221no—
417C4—221no—
418C4—882no—
419C4#1062243412yes—
420C2—21no—
421C2—21no—
422C2—222no—
423C2—441no—
424C2D11×H(3,ℤ/4)11yescharacteristic
425C2#1306832411yescharacteristic
426C2#1306835311yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11C2×#95
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#7951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13066473C2semidirect
5. #13066472C2semidirect
6. #13066471C2semidirect
7. C11×#1285C2semidirect
19. #10622450C4semidirect
21. #10622446C4semidirect
29. #10622318C4semidirect
30. D11×#97C4semidirect
137. #1285D11semidirect
343. C11#7951semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130772462
D11×#4322
#130710122
#130664732
#130664722
#130664712
C11×#12852
#795111